Call a string of letters "legal" if it can be produced by concatenating $($running together$)$ copies of the

following strings:

$\text{'}$v$\text{'},\text{'}$ww$\text{'},\text{'}$xxx$\text{'}\text{'}$yyy$\text{'}$ and $\text{'}zzz\text{'}.$

For example, the string $\text{'}xvv\text{'}$ is legal because it can be produced by concatenating $\text{'}{x}^{\text{'}}\text{'},\text{'}v\text{'}$ and $\text{'}v\text{'},$

but the string $\text{'}v\text{'}$ is not legal.

For each integer $n1,$ let $t_n$ be the number of legal strings with $n$ letters. For example, $t_1=1(\text{'}v\text{'}$ is

the only the legal string$).$

$t_2=$

$t_3=$

$t_n=a{t}_{n-1}+b{t}_{n-2}+c{t}_{n-3}$ for each integer $n4$

where $a=,b=,,$ and $c=$